A244929 Decimal expansion of Ti_2(2+sqrt(3)), where Ti_2 is the inverse tangent integral function.

2, 3, 3, 4, 5, 3, 7, 5, 8, 5, 3, 1, 2, 3, 4, 1, 1, 4, 6, 7, 5, 9, 0, 3, 8, 6, 2, 7, 7, 4, 3, 9, 3, 3, 0, 0, 4, 8, 8, 2, 6, 7, 8, 3, 7, 7, 2, 5, 0, 9, 9, 3, 5, 4, 0, 1, 6, 3, 0, 0, 5, 4, 0, 1, 8, 4, 4, 1, 8, 0, 1, 0, 3, 4, 5, 3, 6, 3, 3, 5, 0, 7, 6, 4, 5, 3, 6, 9, 0, 1, 6, 5, 4, 4, 1, 7, 1, 8, 3, 7, 9, 7, 1, 4, 4

Offset

1,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 1.7.6 Inverse Tangent Integral, p. 57.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Eric Weisstein's MathWorld, Inverse Tangent Integral

Eric Weisstein's MathWorld, Polylogarithm

Formula

2/3*G + 5*Pi/12*log(2+Sqrt(3)), where G is Catalan's number.

Also equals i/2*(polylog(2, -i*(2+sqrt(3))) - polylog(2, i*(2+sqrt(3)))), with i = sqrt(-1).

Example

2.3345375853123411467590386277439330048826783772509935401630054018441801...

Mathematica

2/3*Catalan + 5*Pi/12*Log[2 + Sqrt[3]] // RealDigits[#, 10, 105]& // First

Prog

(PARI) default(realprecision, 100); 2/3*Catalan + 5*Pi/12*log(2 + sqrt(3)) \\ G. C. Greubel, Aug 25 2018
(Magma) SetDefaultRealField(RealField(100)); R:=RealField(); (2/3)*Catalan(R) + 5*Pi(R)*Log(2 + Sqrt(3))/12; // G. C. Greubel, Aug 25 2018

Crossrefs

Cf. A006752, A244928.

Sequence in context: A114544 A154726 A325784 * A302920 A280386 A204979

Adjacent sequences: A244926 A244927 A244928 * A244930 A244931 A244932

Keyword

cons,easy,nonn

Author

Jean-François Alcover, Jul 08 2014

Status

approved